Digital Representation of Audio Information Kevin D. Donohue Electrical Engineering University of Kentucky

Elements of a DSP System Digital Signal Discrete-time Signal Processed Analog Signal Processed Digital Signal Quantizer Analog Signal Coder Computing /Decoding Interpolating /Smoothing

Critical Audio Issues Trade-off between resources to store/transmit and quality of audio information  Sampling rate  Quantization level  Compression techniques

Sound and Human Perception  Signal fidelity does not need to exceed the sensitivity of the auditory system

Audible Frequency Range and Sampling Rate  Frequency range - 20 to 20,000 Hz  Audible intensities - threshold of hearing (1 Pico watt/meter 2 corresponds to 0 db  Sample sweep constant intensity – 0 to 20 kHz in 10 seconds

Sampling Requirement  A bandlimited signal can be completely reconstructed from a set of discrete samples by low-pass filtering (or interpolating) a sequence of its samples, if the original signal was sampled at a rate greater than twice its highest frequency.  Aliasing errors occur when original signal contains frequencies greater than or equal to half the sampling rate.  Signal energy beyond 20 kHz is not audible,  sampling rates beyond 40 kHz should capture almost all audible detail (no perceived quality loss).

Sampling Standards  CD quality samples at 44.1 kHz  DVD quality samples at 48 kHz  Telephone quality 8 kHz.

Spectogram of CD sound

Spectrogram at Telephone Rate Sound

Bandwidth and Sampling Errors  Original Sound  Limited Bandwidth (LPF with 900 Hz cutoff) and sampled at 2 kHz  Original Sound sampled at 2 kHz (aliasing)

Dynamic Range and Audible Sound  Intensity changes less than 1 dB in intensity typically are not perceived by the human auditory system.  25 tones at 1 kHz, decreasing in 3 dB increments  The human ear can detect sounds from 1x to 10 watts / meter 2 (130 dB dynamic range)

Quantization Levels and Dynamic Range  An N bit word can represent 2 N levels  For audio signal an N bit word corresponds to: Nx20xLog 10 (2) dB dynamic range  16 bits achieve a dynamic range of about 96 dB. For every bit added, about 6 db is added to the dynamic range.

Quantization Error and Noise  Quantization has the same effects as adding noise to the signal: AnalogDiscreteDigital  Intervals between quantization levels are proportional to the resulting quantization noise.  For uniform quantization, the interval between signal levels is the maximum signal amplitude value divided by the number of quantization intervals.

Quantization Noise  Original CD clip quantized with 6 bits at original sampling frequency  6 bit quantization at 2 kHz sampling

Encoding and Resources  Pulse code modulation (PCM) encodes each sample over uniformly spaced N bit quantization levels.  Number of bits required to represent C channels of a d second signal sampled at Fs with N bit quantization is: d*C*N*Fs + bits of header information  A 4 minute CD quality sound clip uses Fs=44.1 kHz, C=2, N=16 (assume no header):  File size = (4*60)*2*16*44.1k = Mb (or MBytes)  Transmission in real time requires a rate greater than 1.4 Mb/s

Compression Techniques  Compression methods take advantage of signal redundancies, patterns, and predictability via:  Efficient basis function transforms (wavelet and DCT)  LPC modeling (linear predictive coding)  CLPC (code excited linear prediction)  ADPCM (adaptive delta pulse code modulation)  Huffman encoding

File Formats Critical parameters for data encoding describe how samples are stored in the file ã signed or unsigned ã bits per sample ã byte order ã number of channels and interleaving ã compression parameters

File Formats Extension, name origin variable parameters (fixed; Comments).Au or.snd next, sun rate, #channels, encoding, info string.aif(f), AIFF apple, SGI rate, #channels, sample width, lots of info.aif(f), AIFC apple, SGI same (extension of AIFF with compression).Voc Soundblaster rate (8 bits/1 ch; Can use silence deletion).Wav, wave Microsoft rate, #channels, sample width, lots of info.sf IRCAM rate, #channels, encoding, info None, HCOM Mac rate (8 bits/1 ch; Uses Huffman compression) More details can be found at:

Subband Filtering and MPEG Subband filtering transforms a block of time samples (frame) into a parallel set of narrow band signal

MPEG Layers â MPEG defines 3 layers for audio. Basic model is same, but codec complexity increases with each layer. â Divides data into frames, each of them contains 384 samples, 12 samples from each of the 32 filtered subbands. â Layer 1: DCT type filter with one frame and equal frequency spread per band. Psychoacoustic model only uses frequency masking (4:1). â Layer 2: use three frames in filter (before, current, next, a total of 1152 samples). This models some temporal masking (6:1). â Layer 3: better critical band filter is used (non-equal frequencies), psychoacoustic model includes temporal masking effects, takes into account stereo redundancy, and uses Huffman coder (12:1).

MPEG - Audio Steps in algorithm: â Filters audio signal (e.g. 48 kHz sound) into frequency subbands that approximate the 32 critical bands --> sub-band filtering. â Determine amount of masking for each band caused by nearby band (this is called the psychoacoustic model). â If the power in a band is below the masking threshold, don't encode it. Otherwise, determine number of bits needed to represent the coefficient such that noise introduced by quantization is below the masking effect. â Format bitstream

Example After analysis, the first levels of 16 of the 32 bands are these: Band Level (db) If the level of the 8th band is 60db, It gives a masking of 12 db in the 7th band, 15db in the 9th. Level in 7th band is 10 db ( < 12 db ), so ignore it. Level in 9th band is 35 db ( > 15 db ), so send it. --> Can encode with up to 2 bits (= 12 db) of quantization error